I. Field of the Invention
The present invention relates to a method of designing control laws (e.g., flight control laws in an airplane) by applying a technique called Multi-Input, Multi-Output (MIMO) feedback LTI'zation, which is applicable to solving a feedback control design problem for a class of nonlinear and linear parameter dependent (“LPD”) dynamic systems, also known as linear parameter varying (“LPV”), with multiple inputs and multiple outputs. Feedback LTI'zation combines a co-ordinates transformation and a feedback control law, the results of which cancel system parameter dependent terms and yield the transformed space open loop system linear time invariant (LTI). The present invention further relates to using multi-input feedback LTI'zation to solve the control design problem associated with control systems for LPD dynamic devices. In particular, the invention is applied to a feedback control system for controlling a parameter dependent dynamic device (e.g., an airplane) with multiple control inputs.
II. Background
Design techniques used for solving feedback control design problems can be divided into several classes. For example, two broad classes are (1) Linear Time Invariant systems (herein after referred to as “LTI”) and (2) nonlinear systems. In the last four decades, LTI systems have received a great deal of attention resulting in many well-defined control design techniques. See, e.g., Maciejowski, J. M., Multivariable Feedback Design, 1989, Addison-Wesley and Reid, J. G., Linear System Fundamentals, 1983, McGraw-Hill, each incorporated herein by reference. Nonlinear systems have, in contrast, received far less attention. Consequently, a smaller set of techniques has been developed for use in feedback control system design for nonlinear systems or linear parameter dependent systems. As a result, control law design for nonlinear systems can be an arduous task. Typically, control laws consist of a plurality of equations used to control a dynamic device in a desirable and predictable manner. Previously, designing control laws for LPD systems using quasi-static LTI design techniques could require an enormous amount of effort, often entailing weeks, if not months, of time to complete a single full envelope design. For example, when designing a flight control law, designers must predict and then design the control law to accommodate a multitude (often thousands) of operating points within the flight envelope (i.e., the operating or performance limits for an aircraft).
Feedback Linearization (reference may be had to Isidori, A., Nonlinear Control Systems, 2nd Edition, 1989, Springer-Verlag, herein incorporated by reference), is applicable to control design for a broad class of nonlinear systems, but does not explicitly accommodate system parameter changes at arbitrary rates. Feedback LTI'zation, a technique used for rendering a control system model linear time invariant, for single input systems is outlined in the Ph.D. thesis of the inventor, Dr. David W. Vos, “Non-linear Control Of An Autonomous Unicycle Robot; Practical Issues,” Massachusetts Institute of Technology, 1992, incorporated herein by reference. This thesis extends Feedback Linearization to explicitly accommodate fast parameter variations. However, the Ph.D. thesis does not give generally applicable solutions or algorithms for applying feedback LTI'zation to either single input or multi-input parameter dependent dynamic systems. U.S. Pat. No. 5,615,119 (herein incorporated by reference, and hereafter the “'119”patent) addressed this problem, albeit in the context of failure detection filter design. In particular, the '119 patent describes a fault tolerant control system including (i) a coordinate transforming diffeomorphism and (ii) a feedback control law, which produces a control system model that is linear time invariant (a feedback control law which renders a control system model linear time invariant is hereinafter termed “a feedback LTI'ing control law”).
The '119 patent encompasses fault detection and isolation and control law reconfiguration by transforming various actuator and sensor signals into a linear time invariant coordinate system within which an LTI failure detection filter can be executed, to thus provide a capability for failure detection and isolation for dynamic systems whose parameters vary over time. That is, a detection filter may be implemented in a so-called Z-space in which the system may be represented as linear time invariant and is independent of the dynamic system parameters.
What is needed, however, is the further extension of the feedback LTIzation control law principals in the '119 patent to multi-input parameter dependent systems. Furthermore, control system designers have long experienced a need for a fast and efficient method of designing control laws relating to parameter dependent nonlinear systems. An efficient method of control law design is therefore needed. Similarly, there is also a need for a control system aimed at controlling such a dynamic device with multiple control inputs.